How to make a circular swipe?
Here is another way using beveled curves:


Add a Bezier Circle in Object Mode and press Tab to enter Edit Mode.
With all handles selected press V and select Free.
Select only one handle and press AltC to open the circle.
Press ShiftS and choose Cursor to Selected.
Select the handle on the other side of the opening and press E to extrude and Enter to confirm.
Press ShiftS, and choose Selection to Cursor (Offset) to move the handle to the other side.
Rotate the handle by 90 or 270 degress to get a circular shape (R $Axis $Degress), then leave Edit Mode.
Add a Path in Object Mode. To get a closed slice, scale the Path by .5. Otherwise, &lt; .5.
Select the Bezier Circle again. Under Curve Properties - Geometry - Bevel Object select the name of the newly added Path (e.g. NurbsPath). 
To animate the slice use the Start and End values (Geometry - Bevel Factor).





This should be the result (animated scale of the Path, Start and End values of the Bevel Factor):



Another way could be using the Array Modifier together with the Curve Modifier to get some line effects (similar to the reference you provided).

Starting from a Bezier Circle and a Plane in the same spot, add both modifiers to the Plane. You can play with the scale of the Plane, count and offset of the Array Modifier to get different effects. 



Here some examples: